---
title: "The Major Scale Formula: Whole and Half Steps Explained"
dek: The major scale is seven notes spaced whole, whole, half, whole, whole, whole, half. Here is the formula, four scales built from it, and the sharps and flats it forces.
topic: fundamentals
tags: [major scale, scale, intervals, key signature]
date: 2026-10-11
author: Yunus Emre Vurgun
level: intro
related: [circle-of-fifths-explained, key-signatures-order-of-sharps-and-flats, church-modes-dorian-to-locrian, natural-harmonic-melodic-minor]
faq:
  - q: What is the major scale formula?
    a: Whole, whole, half, whole, whole, whole, half: two semitones, two semitones, one semitone, and so on. Starting that pattern on any note gives a major scale on that note. The pattern is fixed, so the notes change, and the sharps or flats they need follow from it.
  - q: Why does the key of G major have an F sharp?
    a: The sixth and seventh notes need a whole step between them. E to F is only a half step, so the F is raised to F sharp. That makes E to F sharp a whole step and leaves the final F sharp to G as the half step the formula needs.
  - q: How many semitones are in a major scale?
    a: Twelve from the tonic to the octave. The seven steps add up to 2, 2, 1, 2, 2, 2, 1, which is twelve. Each degree sits at a fixed distance from the tonic: 0, 2, 4, 5, 7, 9, 11 and 12 semitones.
  - q: Why does a major scale use each letter name only once?
    a: Each step moves to the next letter name, so seven steps reach seven different letters before the octave returns to the tonic. Accidentals change the pitch of a letter but never add a second copy of it, which keeps the spelling clean.
---

The major scale is a fixed sequence of steps: whole, whole, half, whole, whole, whole, half. A whole step is two semitones and a half step is one. Start the pattern on any note and you have a major scale on that note. The pattern does not change, so the notes do. Where the pattern asks for a step that the natural notes cannot supply, the scale needs a sharp or a flat, and the number of those accidentals tells you which key you are in.

## A whole step and a half step are fixed sizes

On the keyboard an octave holds twelve semitones, one per key, black and white. A half step is one semitone. E to F and B to C have no black key between them, and C to C sharp is one semitone. A whole step is two semitones: C to D skips over one black key. The formula is a pattern of sizes, not of note names, and that distinction is the whole method.

## The formula in degrees and semitones

| Degree | Interval from tonic | Semitones above tonic | Step to the next degree |
| --- | --- | --- | --- |
| 1 | tonic (unison) | 0 | whole |
| 2 | major second | 2 | whole |
| 3 | major third | 4 | half |
| 4 | perfect fourth | 5 | whole |
| 5 | perfect fifth | 7 | whole |
| 6 | major sixth | 9 | whole |
| 7 | major seventh | 11 | half |
| 8 | octave | 12 | returns to the tonic |

The semitone column is the cumulative distance from the tonic, and it is the easiest way to check a scale you have built. Count the semitones and compare them with the list. A scale whose fourth degree sits six semitones above the tonic, rather than five, has a wrong step somewhere.

## Four scales built from the formula

Start on C, the reference, where every step falls on a natural note and no accidentals are needed.

Start on G. The first two steps are whole, G to A and A to B, and the third must be a half step, so B to C is correct and C is the fourth note. C to D and D to E are whole steps. The sixth step needs a whole step, but E to F is only a half step, so the seventh note is raised to F sharp. F sharp to G is then the half step the formula requires. The result is G A B C D E F#, with one sharp.

Start on D. D to E is whole, and so is E to F sharp, so the third note is F sharp. F sharp to G is a half step, as required. G to A and A to B are whole. The sixth step B to C would be a half step, but the formula asks for a whole one, so the seventh note is C sharp. C sharp to D is the final half step. The result is D E F# G A B C#, with two sharps.

Start on F. F to G and G to A are whole steps. The third step must be a half step, and A to B natural is a whole step, so the fourth note is B flat. B flat to C is whole, C to D and D to E are whole, and E to F is the final half step. The result is F G A Bb C D E, with one flat.

Start on Bb. Bb to C and C to D are whole. D to E would be whole, but the formula asks for a half step, so the fourth note is E flat. E flat to F, F to G and G to A are whole, and A to Bb is the final half step. The result is Bb C D Eb F G A, with two flats.

| Tonic | Notes | Accidentals | Key signature |
| --- | --- | --- | --- |
| C | C D E F G A B | none | none |
| G | G A B C D E F# | F# | one sharp |
| D | D E F# G A B C# | F#, C# | two sharps |
| F | F G A Bb C D E | Bb | one flat |
| Bb | Bb C D Eb F G A | Bb, Eb | two flats |

The same logic runs backwards. Take the lowest note of a seven-note collection, measure the steps upward, and check whether they match the pattern. If they do, the collection is the major scale on that note. If they do not, the collection is another mode or a minor scale, and the half steps show where it departs from the major pattern.

## Why every letter appears once

A scale spelled with letter names moves one letter at a time. Each step goes to the next letter, so seven steps reach seven different letters, and the eighth is the tonic again. The formula is then satisfied by altering the pitch of one letter, never by adding a second copy of it. In G major the seventh letter is F, written F sharp because the step needs it. A useful check is that the letters of a major scale run in order, G A B C D E F in G major, with no letter missing and none repeated.

The same logic explains the order of the sharps. Each sharp key adds a sharp on its own seventh degree: G major adds F sharp, D major adds C sharp, and A major adds G sharp. That is why the sharps arrive in the order F C G D A E B, which the [key signature order](/articles/key-signatures-order-of-sharps-and-flats/) article sets out in full.

## The black keys show the pattern on a piano

On the white keys alone, the [C major](/keys/c-major/) scale uses no black keys at all. Its two half steps fall where no black key sits between two white keys: E to F and B to C. Those gaps are the half steps of any major scale, between degrees 3 and 4 and between degrees 7 and 8. A scale on another tonic moves the pattern. In G major the same two gaps still fall at B to C and at F sharp to G, but the seventh note lands on the black key F sharp.

Play the three scales in turn and count the black keys each uses: none, then one, then one. The count is a quick check on any scale you build. In keys with up to five sharps or flats, the number of black keys in the scale equals the number of accidentals the formula demanded.

[keys]C4 D4 E4 F4 G4 A4 B4 C5[/keys]

[keys]G4 A4 B4 C5 D5 E5 F#5 G5[/keys]

[keys]F4 G4 A4 Bb4 C5 D5 E5 F5[/keys]

## Where the formula misleads people

The formula describes the major scale, not every seven-note scale. Starting the same white-key set on D gives a different pattern, whole, half, whole, whole, whole, half, whole, which is the Dorian mode. The church modes article covers the family. Nor does the formula describe a key. A key adds harmonic roles to the scale, and the [circle of fifths](/articles/circle-of-fifths-explained/) shows how keys relate through the sharps and flats they share.

The major sound is not a mood. It comes from the major third, four semitones above the tonic. A minor third is three semitones, and the natural minor scale lowers the third, sixth and seventh degrees by one semitone each. The difference between major and minor is a difference in those intervals.

The formula also assumes equal temperament, in which every whole step is the same size. In just intonation, the two whole steps in a major scale are not equal: the step from the tonic to the second degree can be 9:8, while other whole steps can be 10:9. The sizes in the table are the equal-tempered ones. See [equal temperament](/articles/equal-temperament/) for how the compromise works.

## What to do with it

Choose a tonic that is not in the table, E for example. Write the seven letter names first, E F G A B C D E, then apply the pattern and alter whichever letters it demands. You should arrive at E F# G# A B C# D# and E. Check the result against the semitone list, 0, 2, 4, 5, 7, 9, 11, 12, and then play it on the [virtual piano](/tools/virtual-piano/). Repeat for A flat major, which should give you four flats, and check the count against the [key signature order](/articles/key-signatures-order-of-sharps-and-flats/).